Layer the potatoes, onions, parsnips and 3/4 cup cheese in a greased 13x9-in. baking dish; set aside. In a small saucepan, combine the flour, salt, pepper; gradually whisk in cream. Bring to a gentle boil, stirring occasionally. Remove from the heat; pour over vegetables. Sprinkle with remaining cheese.
Cover and bake at 375° for 30 minutes. Uncover; bake 20-25 minutes longer or until vegetables are tender and top is golden brown.